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The Generalized Backstepping Control Method for Stabilizing and Solving Systems of Multiple Delay Differential Equations

Saja F. Noaman --- Fadhel S. Fadhel

Al-Nahrain Journal of Science مجلة النهرين للعلوم
ISSN: (print)26635453,(online)26635461 Year: 2018 Volume: 00 Issue: 1 Pages: 150-156
Publisher: Al-Nahrain University جامعة النهرين

Abstract

In this paper, a generalized approach of the backstepping method for stabilizing and solving system of ordinary differential equations will be applied for systems of differential equations with multiple delay by transforming the non-linear system of delay differential equations into a system of ordinary differential equations with cooperation of the method of steps. The basic idea of this approach is to find Lyapunov function for stabilizing the system of different time steps which is chosen as the definitions of the present approach.

Keywords

Backstepping control method --- Delay differential equations --- Boundary control problems --- Method of steps --- Stabilization of delay differential equations --- Lyapunov functions.